# Definition and characterization

Definition 10.1.1   Let be a mapping defined over a domain in the complex plane. and let be given .

If preserves the size and the sense of the angle of intersection of any two curves intersecting at , then is called conformal at .

If is conformal at any point of the domain , it is called conformal in .

Theorem 10.1.2   Let be a function analytic over a domain . If is a point of where , the is conformal at .

Noah Dana-Picard 2007-12-24